Applied Mathematics & Optimization

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Invariant Measures for Monotone SPDEs with Multiplicative Noise Term
Applied Mathematics & Optimization - Tập 68 - Trang 275-287 - 2013
Abdelhadi Es-Sarhir, Michael Scheutzow, Jonas M. Tölle, Onno van Gaans
We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller property of the solution to show existence of an invariant measure. As an application we discuss stochastic reaction diffusion equations.
The optimal control of diffusions
Applied Mathematics & Optimization - Tập 22 - Trang 229-240 - 1990
Robert J. Elliott
Using a differentiation result of Blagovescenskii and Freidlin calculations of Bensoussan are simplified and the adjoint process identified in a stochastic control problem in which the control enters both the drift and diffusion coefficients. A martingale representation result of Elliott and Kohlmann is then used to obtain the integrand in a stochastic integral, and explicit forward and backward e...... hiện toàn bộ
Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise
Applied Mathematics & Optimization - Tập 61 - Trang 27-56 - 2009
Wei Liu
The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and fast diffusion equations...... hiện toàn bộ
A note on the structure of optimal stochastic controls
Applied Mathematics & Optimization - Tập 2 - Trang 379-379 - 1975
A. V. Balakrishnan
Optimal Control and Controllability of a Phase Field System with One Control Force
Applied Mathematics & Optimization - Tập 70 Số 3 - Trang 539-563 - 2014
F. D. Araruna, José Luiz Boldrini, Bianca Morelli Rodolfo Calsavara
Sufficient Optimality Conditions in Stability Analysis for State-Constrained Optimal Control
Applied Mathematics & Optimization - Tập 55 - Trang 255-271 - 2007
K. Malanowski
A family of parametric linear-quadratic optimal control problems is considered. The problems are subject to state constraints. It is shown that if weak second-order sufficient optimality conditions and standard constraint qualifications are satisfied at the reference point, then, for small perturbations of the parameter, there exists a locally unique stationary point, corresponding to a solution. ...... hiện toàn bộ
The Stochastic Viscous Cahn–Hilliard Equation: Well-Posedness, Regularity and Vanishing Viscosity Limit
Applied Mathematics & Optimization - - 2021
Luca Scarpa
AbstractWell-posedness is proved for the stochastic viscous Cahn–Hilliard equation with homogeneous Neumann boundary conditions and Wiener multiplicative noise. The double-well potential is allowed to have any growth at infinity (in particular, also super-polynomial) provided that it is everywhere defined on the real line. A vanishing viscosity argument is carried ...... hiện toàn bộ
Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model
Applied Mathematics & Optimization - Tập 64 - Trang 155-169 - 2011
Catherine Donnelly
We prove a sufficient stochastic maximum principle for the optimal control of a regime-switching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be used to solve a mean-variance portfolio selection problem.
Nguyên tắc so sánh cho các phương trình Hamilton-Jacobi loại Dirichlet và nhiễu loạn đặc biệt của các phương trình elliptic suy biến Dịch bởi AI
Applied Mathematics & Optimization - Tập 21 - Trang 21-44 - 1990
G. Barles, B. Perthame
Dưới điều kiện không suy biến trên biên, chúng tôi chứng minh nguyên tắc so sánh cho các sub- và super-solution không liên tục của bài toán giá trị biên Dirichlet tổng quát đối với phương trình Hamilton-Jacobi bậc nhất \({H(x,u,Du) = 0 \text{ trong } \Omega }\) và các điều kiện biên \(Max(H(x,u,Du);u - \varphi ) \geqslant 0 \text{ trên } \partial \Omega\), \(Min(H(x,u,Du);u - \varphi ) \leqslant 0...... hiện toàn bộ
#Hamilton-Jacobi #phương trình Dirichlet #nhiễu loạn đặc biệt #phương trình elliptic suy biến #điều khiển tối ưu
On Nonlocal Variational and Quasi-Variational Inequalities with Fractional Gradient
Applied Mathematics & Optimization - Tập 80 - Trang 835-852 - 2019
José Francisco Rodrigues, Lisa Santos
We extend classical results on variational inequalities with convex sets with gradient constraint to a new class of fractional partial differential equations in a bounded domain with constraint on the distributional Riesz fractional gradient, the $$\sigma $$ -gradient ( ...... hiện toàn bộ
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